I have difficulty in finding numerical integration of a function f(r,t) which is a function of position r and time t. Function f(r,t) consists 100 terms (for example : BesselJ(0, 151.5793716314014*r)+BesselJ(0, 151.5793716314014*r)*r^2+......100 terms). For a particular time t=t1, f(r,t1) is calculated and then integrated as follows:
I am using evalf(Int(f(r,t1),r=0..1)
Maple takes a lot of time to evaluate it as it is integrating it in one shot! Is there a way to
a) pick the terms individually and integrate it
b) then sum these individual terms up together
c) How reliable is evalf(int(f(r,t1),r=0..1)) is? Is evalf (Int()..) the best way to evaluate integration?